Page 251 - 35Linear Algebra
P. 251
13.4 Review Problems 251
(a) Show that Bv is also an eigenvector of A with eigenvalue λ.
(b) Additionally suppose that A is diagonalizable with distinct eigen-
values. What is the dimension of each eigenspace of A?
(c) Show that v is also an eigenvector of B.
(d) Explain why this shows that A and B can be simultaneously diago-
nalized (i.e. there is an ordered basis in which both their matrices
are diagonal).
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